Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+3y &= -8 \\ -9x+y &= 4\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {9x+4}$ Substitute this expression for $y$ in the first equation. $3x+3({9x + 4}) = -8$ $3x + 27x + 12 = -8$ Simplify by combining terms, then solve for $x$ $30x + 12 = -8$ $30x = -20$ $x = -\dfrac{2}{3}$ Substitute $-\dfrac{2}{3}$ for $x$ back into the top equation. $3( -\dfrac{2}{3})+3y = -8$ $-2+3y = -8$ $3y = -6$ $y = -2$ The solution is $\enspace x = -\dfrac{2}{3}, \enspace y = -2$.